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Abstract: It is well known that the solution of the equality constrained least squares (LSE) problem min Bx=d kb \Gamma Axk2 is the limit of the solution of the unconstrained weighted least squares problem fl fl fl fl fl as the weight tends to infinity, assuming that [ B ] has full rank. We derive a method for the LSE problem by applying Householder QR factorization with column pivoting to this weighted problem and taking the limit analytically, with an appropriate rescaling of rows. ... (Update)
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BibTeX entry: (Update)
A. J. Cox and N. J. Higham. Row-wise backward stable elimination methods for the equality constrained least squares problem. Numerical Analysis Report No. 319, Manchester Centre for Computational Mathematics, Manchester, England, Mar. 1998. To appear in SIAM J. Matrix Anal. Appl. http://citeseer.ist.psu.edu/article/cox00rowwise.html More
@techreport{ cox98rowwise,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Row-Wise Backward Stable Elimination Methods for the Equality Constrained Least Squares Problem",
number = "No. 319",
address = "Manchester, England",
pages = "18",
year = "1998",
url = "citeseer.ist.psu.edu/article/cox00rowwise.html" }
Citations (may not include all citations):99 Society for Industrial and Applied Mathematics (context) - Higham, Stability et al. - 1996
62 Manchester Centre for Computational Mathematics (context) - Higham, Matrix et al. - 1995
34 the compatibility of a given solution with the data of a lin.. (context) - Rigal, Gaches - 1967
15 Iterative refinement of linear least squares solutions II (context) - Bjorck - 1968
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11 Error analysis and implementation aspects of deferred correc.. (context) - Barlow - 1988
9 On applying Householder transformations to linear least squa.. (context) - Powell, Reid - 1968
8 Stability of Householder QR factorization for weighted least.. - Cox, Higham - 1997
8 The direct solution of weighted and equality constrained lea.. (context) - Barlow, Handy - 1988
6 Accuracy and stability of the null space method for solving .. - Cox, Higham - 1997
6 Society for Industrial and Applied Mathematics (context) - Lawson, Hanson et al. - 1995
6 the method of weighting for equality-constrained least-squar.. (context) - Van Loan - 1985
5 Backward error analysis for the constrained and weighted lin.. (context) - Gulliksson - 1995
5 Modifying the QR-decomposition to constrained and weighted l.. (context) - Gulliksson, Wedin - 1992
5 the weighting method for least squares problems with linear .. - Stewart - 1997
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